A First Course in Algebraic Topology by Czes Kosniowski PDF

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A first course in algebraic topology written by Czes Kosniowski This is an other great mathematics book cover the following topics.

Sets and groups

Metric spaces, Topological spaces, Continuous functions

Induced topology, Quotient topology (and groups acting on spaces)

Product spaces, Compact spaces, Hausdorff spaces, Connected spaces

The pancake problems

Manifolds and surfaces

Paths and path connected spaces, The Jordan curve theorem

Homotopy of continuous mappings

'Multiplication' of paths

The fundamental group, The fundamental group of a circle

Covering spaces, The fundamental group of a covering space, The fundamental group of an orbit space

The Borsuk-Ulam and ham-sandwhich theorems, More on covering spaces: lifting theorems, More on covering spaces: existence theorems

The SeifertVan Kampen theorem: I Generators; II Relations; III Calculations

The fundamental group of a surface

Knots: I Background and torus knots, Knots : II Tame knots, Table of Knots

Singular homology: an introduction

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